*2.3. Boundary Conditions and Unsteady Simulation*

The boundary conditions used for the simulation were obtained from a report on a GE-E<sup>3</sup> performance test [15], shown in Table 2. Ideal gas was used as the working fluid. Total pressure and temperature were set for the inlet, while static pressure was specified for the outlet. The magnitude of the total pressure used for the inlet was 344,740 Pa, with a uniform turbulence intensity of 5%. A non-uniform temperature, which was considered as the HS condition, was applied. The maximum and average temperatures of the HS were approximately 839 and 728 K, respectively. The detailed profile of the HS is shown in Figure 4. The static pressure specified for the outlet was 104,470 Pa. The speed of the rotor blade was fixed at 3600 rpm. Furthermore, to investigate the effects of rotor blade damage coupled with HS conditions, we analyzed five rotor blades cases. An undamaged rotor blade was considered as the reference case. The other cases were damage (i) at the middle of the blade on the pressure side, (ii) at the middle of the blade on the suction side, (iii) at the top of the blade on the pressure side, and (iv) at the top of the blade on the suction side. Moreover, we conducted both adiabatic and isothermal condition tests for the blade surface to calculate the heat transfer characteristics. The temperature applied to the blade surface under isothermal conditions was set as 389.95 K.


**Table 2.** Boundary conditions and simulation settings.

(**a**) (**b**)

To perform an unsteady simulation, it is necessary to conduct a steady simulation, the results of which are used as an initial condition for the unsteady simulation. A frozen rotor was set as the interface between the stator and rotor in the steady simulation. The unsteady simulation was performed with a transient rotor-stator setting for the rotor–stator interface. To obtain accurate results in the unsteady simulation, the appropriate number of time steps per pitch—the number of steps when one rotor blade passes a pitch of the stator—needs to be considered. Previous studies have confirmed that 32 steps are the most suitable to guarantee convergence in such unsteady simulations [9,10].

In this study, we used a total of 20 pitches for the unsteady simulation as the results started to become periodic after 10 pitches. The first 10 pitches were considered to be the initial transient condition, and the final 10 pitches were used to analyze the results. We set several monitoring points near the pressure side of the blade and vane to check the convergence history. When the pressure and temperature of monitored points started to exhibit periodicity, the unsteady simulations were considered to have become convergent. The simulations were conducted using a 96-core workstation (4 Intel Xeon CPU E7-8890 v4 @ 2.20 GHz, RAM 512 GB), and the time needed for an unsteady simulation was approximately 72 h using 60 cores.
